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9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0 is prime. [Silva] If the digit sum of n!, S(n!), is the product of 9 and any prime larger than n, then S(n!) cannot divide n!. All digits of the prime 2 * 10^{3020}  1 are 9 except 1. It contains 3021 digits. [Williams] The sum of the first 9 consecutive prime numbers = 10^{2}, a perfect square. If odd perfect numbers exist, they are of the forms 12n + 1 ... or 36n + 9. [Touchard] 9 is the smallest "April Fool prime." For every prime p with p not equal to 2 and p not equal to 5, there is some number with all digits equal to 9 such that p divides evenly into this number. Goldbach conjectured that every odd integer greater than or equal to 9 can be represented as the sum of three odd primes. There are no consecutivedigit primes starting with 9 with digits in descending order. [Madachy] Define a certain number of irregularly marked points, n, along the rim of a paper circle, then cut along straight lines that join all possible pairs of points. If n = 9, a prime number of separate pieces will be created. 163 to be exact! The smallest odd Giuga number must have at least 9 prime factors. If a is greater than b, and b is greater than or equal to 1, then a^{n} + b^{n} has a primitive prime factor with the exception of 2^{3} + 1^{3} = 9. 9 times the 9th prime has a sum of digits equal to 9. There are no clusters (groups) of 9 twin prime pairs less than 10^{14}. [DeVries] Washington University in St. Louis provides a page that calculates the prime factors of a number (with a maximum of 9 digits). There are at least 9 prime numbers between x^{3} and (x + 1)^{3} for x greater than or equal to , assuming the Riemann Hypothesis is true. The smallest odd composite number. [Gupta] 10^{9} + 9 is prime. [Gupta] Two raised to the 9th power plus and minus 9 are primes! [Hoefakker] The first digit to appear as an enddigit in two consecutive primes (139 and 149). [Silva] 19, 109, 1009 and 10009 are primes. No other digit can replace the 9 and yield four primes. [Friend] The number of known positive integers which are the sum of two primes in exactly two ways is a prime square. [Capelle] 2^^n9 = 2^(2^(2^(....(2^2)...)))9 is (for large enough n) always divisible by both 7 and 11. Note that 9 is midway between 7 and 11. [Hartley] There are exactly 3=(sqrt(9)) pandigital improper fractions that reduce to 9 (provided each digit is used once). [Patterson] 9 is the only number m such that m = ((m)!). [Firoozbakht] The 9th Fibonacci number plus 9 is prime. [Losnak] The only composite digit that can appear as enddigit of a prime. [Silva] The only nonprime digit that is the difference of consecutive squares. [Silva] 10*(2^{2n} + 1) + 9 gives primes for n = 1 to 7. Therefore, there are 7 known Fermat numbers which yields primes when a 9 is appended. [Wesolowski] The smallest composite number n such that both 2^{n}+n and 2^{n}n are prime. That is, 2^{9}+9 = 521 and 2^{9}9 = 503 are prime. [Poo Sung] 9+8^7+6^5+4^3+2^1 is prime. [Silva] Three more semiprimes can be consecutively formed from 9 by iterating the process described in A227942. The only known integer n, such that 2^nn^2 and 2^n+n^2 are both primes, i.e., 431 and 593. [Loungrides]
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